This invention relates generally to communicating data securely, and more particularly to a cryptographic system and methods of using public key cryptography.
Computer systems are found today in virtually every walk of life for storing, maintaining, and transferring various types of data. The integrity of large portions of this data, especially that portion relating to financial transactions, is vital to the health and survival of many commercial enterprises. Individual consumers also have an increasing stake in data security as open and unsecure data communications channels for sales transactions, such as credit card transactions over the Internet, gain popularity.
Protecting data stored in computer memory, tape, and disk is often important. However, just as important, if not more so, is the ability to transfer financial transactions or other communications from a sender to an intended receiver without intermediate parties being able to interpret the transferred message. Furthermore, as important transactions are increasingly handled electronically, authentication of the originator of a message must be ensured. For example, for electronic banking, there needs to be a way to authenticate that an electronic document, such as a bank draft, has actually been “signed” by the indicated signatory.
Cryptography, especially public key cryptography, has proven to be an effective and convenient technique of enhancing data privacy and authentication. Data to be secured, called plaintext, is transformed into encrypted data, or ciphertext by a predetermined encryption process of one type or another. The reverse process, transforming ciphertext into plaintext, is termed decryption. In public key cryptography, the processes of encryption and decryption are controlled by a pair of related cryptographic keys. A “public” key is used for the encryption process, and a “private” key is used to decrypt ciphertext. Alternatively, the private key may be used to encrypt the data, and the public key to decrypt it. This latter method provides a method of digitally signing data to positively identify the source of the data.
The prior art includes a number of public key schemes. However, over the past decade, one system of public key cryptography has gained popularity. Known generally as the “RSA” scheme, it is now thought by many to be a worldwide defacto standard for public key cryptography. The RSA scheme is described in U.S. Pat. No. 4,405,829.
The RSA scheme capitalizes on the relative ease of creating a composite number from the product of two prime numbers whereas the attempt to factor the composite number into its constituent primes is difficult. Pairs of public/private keys can then be found based on the factors of the composite number. A message is encrypted using a series of mathematical exponentiations and divisions based on one of the keys. If the matching key of the public/private key pair is known, the message can be decrypted using a series of mathematical exponentiations and divisions using the matching key. The composite number is a part of the public and private keys and is known to the public. However, since the private key can only be found by factoring the composite number, calculating the private key from the public key is computationally difficult.
The security of the RSA technique can be enhanced by increasing the difficulty of factoring the composite number through judicious choices of the prime numbers. (This, of course, would be true for any encryption/decryption scheme using or requiring prime numbers.) Another, and principle enhancement, is to increase the length (i.e., size) of the composite number. Today, it is common to find RSA schemes being proposed in which the composite number is on the order of 600 digits long. The task of exponentiating a number this long, however, can be daunting and time consuming, although not as difficult as factoring. Therefore, increasing the length of the composite number increases the security, but only at the expense of increased time to perform the encryption and decryption.
However, recently discovered techniques have greatly improved the efficiency with which encryption/decryption functions are performed using the RSA scheme. Rather than using two prime numbers to form the composite number conventionally employed in RSA cryptographic operations, it has been found that more than two prime numbers can also be used. In addition, it has also been found that the Chinese Remainder Theorem can be used to break an RSA encryption or decryption task into smaller parts that can be performed much faster than before.
The Chinese Remainder Theorem allows the necessary computations to be divided into two exponentiations. Commonly assigned U.S. Pat. No. 5,848,159, filed Jan. 16, 1997, which is incorporated by reference for all purposes, discloses a method of using multiple prime numbers to create the composite number and further dividing the exponentiations into multiple smaller exponentiations. However, though the encrypting and decrypting exponentiations are smaller and therefore accomplished more quickly, the factorization of the composite number is no easier to compute. So, the security of the system is not compromised.
In addition to the security of the data, another important issue with regard to cryptographic systems is the security of the system itself and processes handled thereby. In a system implementing an encryption algorithm, ensuring that the system is secure from tampering is important. One area of concern is the secure loading and storing of application programs for the system. If the application program can be altered or substituted, the security of a system may be breached.
It is therefore desirable to provide an efficient cryptographic system for implementing public key cryptography with multiple prime factors. It is also desirable to provide a cryptographic system that may be initialized to a secure state and can provide security and maximum flexibility for user application programs.